"As far as the lock differential, would anyone know where that is located, or is that just the brake locks? I have also noticed that near the gas pedal there is a pedal that I cannot figure out what it does. Maybe that has something to do with the problem?"
On my tractor, the differential lock comes out of the panel just below the driver's seat (this is a Deere 790). It should only be used if one rear tire is turning and the other is not. The purpose is to lock the axles to both rear wheels to increase traction. The differential lock should only be used if one is operating in a straight line (no turns). Once engaged, the differential lock will remain engaged until the traction is equalized on both rear tires, then it should disengage itself. You could try operating the machjine in reverse...if the lock is sticking, that may break it loose.
I suppose this could be the problem...the differential lock not disengaging...as the rear wheels will try to drive the tractor in a straight line. That's really just a guess.
At this point, I'd ask the friend you borrowed the tractor from if he has a manual (although I'd of thought he would have brought it with him when you tried to troubleshoot). If he doesn't have one, you may have to ask the friend to connect you with whoever maintains his tractor. I'm hoping he does know someone...
If the differential lock is stuck in the engaged position, it may just be the linkage is frozen up (rust or lack of lubrication).
The trouble is, unless you have a reasonably good idea of what is causing the problem, you could make it worse. Or, you could just operate the tractor and see what happens.
I know this puts you in a bad position with your friend...however, there probably won't be any responses on TBN other then guesses (as I'm doing).